Electrophotographic apparatus

ABSTRACT

An electrophotographic apparatus comprises a photosensitive screen drum of a radius r 1  having a number of apertures formed therein and rotating through a printing or charging area having a width W at a constant peripheral velocity v 1 , a record medium such as a charge transferring drum of a radius r d  (r 2  = r 1 ) arranged opposite to the screen drum with a distance d at the printing area and rotating through the printing area at a constant peripheral velocity v 2 , means for forming on the screen drum an electrostatic latent image of a document to be copied, and means for generating a corona ion stream passing in the printing area through the apertures of the screen drum, whereby the corona ion stream is modulated with an electric field formed in or near the apertures of the screen drum so as to form on the transferring drum a charge image corresponding to the latent image on the screen drum. The screen drum and transferring drum are rotated at a velocity ratio k = v 2  /v 1  which satisfies the following equation. ##EQU1## When the record medium is a copy paper, it is fed through the printing area along an arcuate passage having the radius r 2  at the constant peripheral velocity v 2 .

BACKGROUND OF THE INVENTION

The present invention relates to an image forming apparatus andparticularly to an electrophotographic apparatus of a type using aphotosensitive screen having a number of small apertures.

In such an electrophotographic apparatus on the photosensitive screenthere is formed an electrostatic latent image corresponding to adocument to be copied. For this purpose the photosensitive screen isusually formed by applying on a conductive metal mesh a photoconductivelayer, an insulating layer, a conductive layer, etc.

It has been known from, for example Japanese Patent Publication Nos.30,320/70 and 11,579/74 and Japanese Patent Laid-Open Publication Nos.84,640/73 and 59,840/73 to form an electrostatic latent image on adielectric record paper by passing an ion stream through the fineapertures of the screen, said ion stream being modulated with variouselectric fields produced in or near the apertures or to form a coloredimage on a plain paper by selectively charging floating ink particles bymeans of the modulated ion stream.

Further in usual electrophotographic apparatus it has been widelypractised that the photosensitive body is formed as a drum and a tonerimage on the photosensitive drum is transferred onto a plain paper or alatent image on the drum is transferred onto an electrostatic copy paperor a coated paper.

In thse known copying systems the photosensitive drum and a copyingpaper are traveled in an intimately contact manner and circumferentialvelocities of the drum and copy paper should be made equal to eachother.

Further in the known systems an area or range where the transferring iseffected is limited to an area in which the drum is substantially incontact with the transferring paper. This area is sometimes referred toas a printing or charging area.

It is also known from, for example Japanese Patent Publication No.21,142/72 that the above mentioned photosensitive screen is formed as adrum and an image is formed on the record medium which travels throughthe printing area along a flat passage.

The present inventors have found that in order to effect an excellentcopying with such an image forming apparatus of screen drum type acharging or printing width (measured in the traveling direction ofrecord medium) produced by a printing corona charger must be verynarrow. That is to say the width of the corona ion stream must beextremely small. If the printing width is made wide, image forming dotson the record medium are prolonged or expanded in the travelingdirection of the record medium. Thus the definition or resolution of thecopied image might be decreased. On the other hand if the printing widthis made narrow, the printing speed has to be lowered and thus it isquite difficult to realize a high speed electrophotographic apparatuswhich is earnestly desired by many customers.

As explained above it is very difficult to find a solution whichsatisfies the above mentioned two mutually contradictory problems.

SUMMARY OF THE INVENTION

The present invention has for its object to provide a novel and usefulelectrophotographic apparatus of the kind using the photosensitivescreen, in which use can be made of a charging or printing width as wideas possible and thus a high speed copying can be effected withoutdeterioration of the image resolution by suitably determining a ratio ofperipheral velocities of the photosensitive screen and the record mediumin the printing area.

The electrophotographic apparatus according to the invention comprises aphotosensitive screen having a number of fine apertures formed thereinand traveling through a printing area along an arcuate passage having aradius r₁ at a constant peripheral velocity v₁ ; a record mediumarranged opposite to the photosensitive screen with the minimum distanced in the printing area and traveling through the printing area along anarcuate passage having a radius r₂ (r₂ ≠ r₁) at a constant peripheralvelocity v₂ ; means for forming on the photosensitive screen anelectrostatic latent image corresponding to a document to be copied; andmeans for generating a corona ion stream which passes in the printingarea through the apertures of the screen to the record medium and has aprinting or charging width W; wherein a ratio k of the peripheralvelocities v₁ and v₂ of the photosensitive screen and record mediumsatisfies the following condition; ##EQU2##

In a preferred embodiment of the invention said ratio k substantiallysatisfies the following condition;

BREIF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagrammatic view showing an embodiment of theelectrophotographic apparatus according to the invention;

FIG. 2 is a diagram illustrating lines of electric force generatedbetween a photosensitive screen drum and a transferring drum;

FIG. 3 is a diagram also showing the line of electric force;

FIG. 4 is a graph showing a ratio of peripheral velocities of the screendrum and transferring drum with respect to a position in a printingarea;

FIG. 5 is a diagram illustrating a relation between the ratio of theperipheral velocities of the screen drum and transferring drum andamounts of dot prolongation;

FIG. 6 and FIG. 7 are graphs showing a relation between the peripheralvelocity ratio and amounts of dot prolongation; and

FIG. 8 is a graph illustrating a relation between the minimum dotprolongation and the peripheral velocity ratio.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 1 illustrates diagramatically a whole construction of an embodimentof an electrophotogrphic apparatus according to the invention. In thepresent embodiment a photosensitive screen is formed as a drum 1. Thescreen drum 1 is formed by applying on a conductive metal mesh aphotosensitive layer, an insulating layer, a conductive layer, etc. Thescreen drum 1 is arranged to rotate in an anti-clockwise direction at aconstant speed. Along the circumference of the screen drum 1 is arrangeda first corona charger 3 which charges homogeneously the screen drum 1.The homogeneously charged screen drum 1 is next subjected to an exposureof a document image at a light image exposing area 4 by means of asuitable image projecting system. A document stage 5 is made movable ina horizontal direction and a document 6 to be copied is placed on thestage 5. The document 6 is illuminated by a illuminating system 7provided underneath the stage 5. A light reflected from the document 6is projected onto the screen drum 1 by means of a mirror 8 and aprojection lens 9. Then the homogenous charge on the screen drum 1 isselectively discharged in accordance with the projected light image soas to form on the screen drum 1 an electrostatic latent imagecorresponding to the light image of the document 6.

The screen drum 1 further rotates and comes into a printing or chargingarea at which a second corona charging device 10 is arranged. Thisprinting corona charger 10 is arranged inside the screen drum 1 andgenerates an ion stream through meshes or fine apertures formed in thescreen drum 1 to a record medium 11. In this embodiment the recordmedium 11 is formed as an electrostatic charge transferring drumarranged opposite to the second corona charger 10 with respect thescreen drum 1. The record medium 11 is rotated in a clockwise directionat a constant speed. During the corona ion stream passes through thescreen drum 1 the ion stream is modulated with electric fields formed inor near the apertures of the screen drum 1 in accordance with the latentimage on the screen drum 1. Thus a secondary latent image correspondingto the primary latent image on the screen drum 1 is formed on the recordmedium 11.

As the record medium, i.e. transferring drum 11 rotates the latent imagethereon is developed by toners at a developing device 12 and then thedeveloped toner image is transferred onto a plain paper which is fedfrom a paper cassette 14. For effecting the transferring efficientlythere is arranged a corona charger 13 which supplies corona ions ontothe back of the paper. The transferred toner image on the paper is nextthermally fixed by means of a heat roller 15. The paper having the tonerimage fixed is discharged onto a tray 16.

The transferring drum 11 is cleaned by a cleaning brush 17 to which anair suction is applied. Near the cleaning brush 17 is arranged anerasing corona charger 18 which cancels the electrostatic residualcharge on the transferring drum 11 or charges homogeneously the drum 11at a low potential of the same polarity as that of the toners. If aninsulating surface layer of the transferring drum 11 is made ofphotosensitive material, the above mentioned discharging or erasingprocess may be carried out by means of light. The developing,transferring, fixing, cleaning, etc. are not essential for the presentinvention and any other processes may be utilized.

The screen drum 1 is surrounded by a cover 19 which makes the drum freefrom stray light, dust, etc. Moreover in the projecting optical systemthere may be included a concave or convex cylindrical lens 20 so as tocompensate a unilateral distortion of the copied image due to adifference in diameters of the screen drum 1 and the transferring drum11.

After a single copy is obtained the screen drum 1 further rotates and isagain charged homogeneously by the first corona charger 3 and the aboveexplained operations are repeated so as to make successive copies.

In the electrophotographic apparatus of the kind mentioned above thesurface of the screen drum 1 on which the primary latent image has beenformed travels through the charging or printing area along an arcuatepassage having a radious r₁ and the record medium 11 passes through theprinting area also along an arcuate passage having a radius r₂.Therefore if peripheral velocities v₁ and v₂ of the screen drum 1 andthe record medium 11 are equal to each other and the radii r₁ and r₂ areequal to each other, the charge dots forming the secondary latent imageon the record medium 11 tend to prolong or expand in the travelingdirection of the record medium 11 during the passage though the printingarea. Therefore the resolution of the copy image is liable to decrease.In order to minimize such dot expansion or prolongation it is necessaryto determine an optimum relation between the velocities v₁ and v₂ withtaking into account of the finite charging or printing width of theprinting corona generator 10.

FIG. 2 illustrates in a simplified manner how to generate lines ofelectric force between the screen drum 1 having the radius r₁ and acenter O₁ and the record medium 11 having the radius r₂ and a center O₂.It is certified by solving a Pisson's equation and applying a conformalmapping theory that when two conductive cylindrical bodies are arrangedin parallel with each other, the electric field outside thesecylindrical bodies is identical with a field which would be formed by apair of imaginary conductive wires (extending in parallel to thecylindrical bodies) passing through points F₁ and F₂ situated on asegment between the centers O₁ and O₂. Further in this case the lines ofelectric force outside the cylindrical bodies correspond to cylindricalsurfaces having a center O on a straight line which bisects verticallythe segment F₁ F₂. Thus the ion stream passing through a point A₁ on thescreen drum 1 travels along the line of electric force and reaches apoint A₂ on the record medium 11. In the same manner the ion streamspassing through points B₁ and C₁ move along the lines of electric forcepassing through the points B₁ and C₁, respectively and reach the recordmedium 11 at points B₂ and C₂, respectively.

Since the surface of the cylindrical body has the same potential, when apoint P₁ is selected on the cylindrical body having the center O₁, aratio of segments F₁ P₁ and F₂ P₁ is made constant.

    (F.sub.1 P.sub.1 /F.sub.2 P.sub.1) = constant              (1)

When particular points A₁ and A₁ ' are selected as the point P₁, saidpoints A₁ and A₁ ' being intersecting points of the straight linepassing through the center O₁ and O₂ and the cylindrical body 1, thefollowing relation can be obtained:

    (F.sub.1 A.sub.1 /F.sub.2 A.sub.1) = (F.sub.1 A.sub.1 '/F.sub.2 A.sub.1 ') (2)

now it is defined that OA₁ = d₁, OA₂ = d₂ (therefore d₁ + d₂ = d) andOF₁ = OF₂ = f, then the equation (2) can be rewritten as follows:##EQU4## In a similar manner when points A₂ and A₂ ' are selected as apoint P₂ on the cylindrical body 11, said points A₂ and A₂ ' beingcrossing points between the line passing through the centers O₁, O₂ andthe cylindrical body 11, the following equation can be obtained:

    (F.sub.2 A.sub.2 /F.sub.1 A.sub.2) = (F.sub.2 A.sub.2 '/F.sub.1 A.sub.2 ') (4)

from this equation (4) one can obtain the following equation: ##EQU5##

From the equations (3) and (5) there can be derived the followingequation between d₁ and d₂ by canceling f.

    d.sub.1 (2r.sub.1 +d.sub.1) = d.sub.2 (2r.sub.2 + d.sub.2) (6)

Upon considering d₁ + d₂ = d this equation can be written as follows:##EQU6##

FIG. 3 shows the screen drum 1 (radius r₁) and the record medium 11(radius r₂) in the simplified manner. In FIG. 3 tangential lines passingthrough points B₁ and B₂ intersect at a single point G with the linewhich bisects the segment F₁ F₂. An arc B₁ B₂ on a circle having acenter G and a radius GB₁ = GB₂ = R represents a line of electric forcefrom the point B₁ to the point b₂. θ₁ represents an angle made bysegments O₁ B₁ and O₁ A₁ and θ₂ an angle made by segments O₂ B₂ and O₂A₂. Further the screen drum 1 and record medium 11 rotate in mutuallyopposite directions at circumferential velocities v₁ and v₂,respectively. From FIG. 3 the following relations can be derived.

    r.sub.1 cosθ.sub.1 + R sinθ.sub.1 = r.sub.1 + d.sub.1 (8)

    r.sub.2 cosθ.sub.2 + R sinθ.sub.2 = r.sub.2 + d.sub.2 (9)

From these equations the following equation can be obtained with respectto θ₁ and θ₂ by deleting R. ##EQU7## Wherein α is given by the followingequation: ##EQU8##

Now it may be considered that θ₁ and θ₂ (measured as radian unit) aresmaller than 1 in usual case. Therefore where the equations (10) and(11) are expanded into power series and θ₂ is represented by takingthird order of θ₁, the following approximation can be obtained: ##EQU9##

By substituting d₁, d₂ in this equation for those given by the equation(7) the equation (12) can be rewritten into as follows: ##EQU10##

Since an arc A₁ B₁ = r₁ θ₁ and an arc A₂ B₂ = r₂ θ₂, the equation (13)can be further rewritten into the following equation: ##EQU11##

Thus one can obtain the following equation: ##EQU12##

Further since the peripheral velocities v₁ and v₂ can be expressed as##EQU13## respectively, a ratio of these velocities v₂ /v₁ can berepresented as follows: ##EQU14##

If the record medium 11 is made flat at the printing or charging area,the equations (15) and (16) can be rewritten into the followingequations (17) and (18), respectively by marking r₂ infinite: ##EQU15##

The equations (15) and (16) can be represented by curves A, A', B and B'in a graph shown in FIG. 4, in which an abscissa represents θ₁ and anordinate (A₂ B₂ /A₁ B₁) and v₂ /V₁). In this graph a line C represents afirst term of the equations (15) and (16), i.e. ##EQU16##

These curves make apparent the fact that in a range of small θ₁ theratio of speeds (v₂ /V₁) can be equal to the ratio of arcs (A₂ B₂ /A₁B₁). But as θ₁ becomes larger the curves B and B' become apart from theline C.

Now it is considered that the expansion or prolongation of the chargedots should be made as small as possible within a certain θ₁corresponding to a finite charging width. As far as a single dot isconcerned it is possible to delete the expansion by changing the speedv₂ of the record medium 11 as shown by the curves B or B' in FIG. 4.But, in fact, a great number of dots are printed simultaneously and thusthe remaining dots are prolonged even by changing the speed v₂ as statedabove. Thus the record medium 11 should be rotated at a constant speed.Now the inventors have found that the prolongation or expansion ofcharge dots could be reduced to such an extent that the dot prolongationdoes not practically affect the quality of the copied image by selectingthe ratio v₂ /v₁ of the peripheral velocities of the screen drum 1 andthe record medium 11 substantially as shown by a line D which isdifferent from the line B for a given value of the charging or printingwidth θ₀. This will be explained in greater detail hereinafter.

FIG. 5 illustrates a relation between the circumferential velocity v₂ ofthe record medium 11 and an amount Δ of the dot prolongation orexpansion. For the sake of simplicity only a case of r₂ > r₁ is shown inFIG 5, but the similar relation is existent in case of r₂ < r₁. In FIG.5 the charging width is equal to 2θ₀ and the screen drum 1 and therecord medium 11 rotate at the constant speeds v₁ and v₂, respectivelyin the opposite directions as shown by arrows.

Now it is assumed that a point P on the screen drum 1 comes into thecharging or printing area at a point C₁. The ion stream running from thepoint C₁ of the drum 1 to the record medium 11 forms a sharp charge doton the record medium 11 at a point C₂ independent of the value of v₂(because the speed of the ion stream is sufficiently higher than v₁ andv₂). Then the dot becomes prolonged in a course that the point P passessuccessively points A₁ and B₁. An amount of the dot expansion depends onthe speed v₂. For example, consider a case of v₂ = v₁ = r₁ θ ₁. When thepoint P moves into the point A₁, a dot position found at the point A₂(shown by solid black dot) preceeds to a dot position formed at thepoint A₁ (shown by a small circle), because a traveling speed of a legporton of the line of electric force on the record medium is higher thanthe rotating speed v₂ of the record medium. This tendency becomes largeras the point P moves further toward the point B₁. In this manner theprolongation or expansion of the charge dot which has been formed afterthe point P has traveled over the whole charging or printing area 2θ₀becomes extremely large.

Similarly when it is selected that ##EQU17## the dots formed during thepoint P moves through the points A₁, B₁ preceed to the dot formed at thepoint C₂. However in this case the moving speed of the leg portion ofthe line of electric force on the record medium 11 is substantiallyequal to the traveling speed of the record medium at a vicinity of thepoint A₂ and thus the amount of dot prolongation is smaller than thatproduced in case of v₁ = v₂. On the other hand if it is determined that##EQU18## the rotating speed of the record medium is always higher thanthe traveling speed of the leg portion of the line of electric force onthe record medium. Thus the dot positions formed during the point Pmoves through the points C₁, A₁ and B₁ succeed the dot position which isformed at the point C₂. Therefore the direction of the dot prolongationis opposite to that of the previous case. At any rate the prolongationor expansion of dot occurs.

The nature of dot prolongation has been explained hereinbefore withreference to the three cases. Now a particular value of v₂ which canmake the amount of dot prolongation minimum will be explained. For thesake of simplicity the following analysis will be made for only case ofr₂ >r₁, but the similar analysis may be effected also for a case of r₂ <r₁. In the latter case only results are shown.

Now it is assumed that the circumferential velocity v₂ of the recordmedium 11 is higher than the circumferential velocity v₁ of the screendrum 1 by k times, that is to say v₂ = kv₁. Then in FIG. 3 the point A₂rotates over a distance kv₁ t within a time period t. ##EQU19## Then anamount δ(θ₁) of the dot prolongation can be represented as follows:##EQU20## It should be noted that the equation (20) can be obtained fora case that θ₁ is denoted as shown in FIG. 3. In order to consider theactual dot prolongation it is preferrable to select in such a mannerthat a zero point θ₀ = 0 lies on the segment O₁ C₁. Then the finitecharging or printing area can be represented by 2θ₀ and a domain ofvariability of θ₁ becomes 0 ≦ θ₁ ≦ ₀. When θ₁ is converted into θ₁ - θ₀and δ(θ₁) into δ(θ₁) - δ(θ_(o)), the equation (20) can be rewritten intoas follows: ##EQU21##

This equation can be further summerized into ##EQU22##

In the equations (20) and (21) k can be any value. Now several exampleswill be explained with various values of k. ##EQU23## In case of r₂ <r₁, since α < 0 and β < 0, the following equation can be obtained:

    δ(θ.sub.1) = -θ.sub.1 {|β|θ.sub.1.sup.2 -3|β|θ.sub.0 θ.sub.1 +(|α|+3|β|θ.sub.0.sup.2)}                                                       (22)'

The equations (22) and (22)' are represented by a curve a in FIG. 6 andby a curve a in FIG. 7, respectively. ##EQU24## These equations (25) and(25)' are shown by curves b in FIGS. 6 and 7, respectively. ##EQU25##The following equations can be derived:

    δ(θ.sub.1) = βθ.sub.1 {θ.sub.1.sup.2 - 3θ.sub.0 θ.sub.1 + 3(θ.sub.0.sup.2 - θ.sub.x.sup.2)}                                     (26)

In case of r₂ < r₁

    δ(θ.sub.1) = -|β|θ.sub.1 {θ.sub.1.sup.2 - 3θ.sub.0 θ.sub.1 + 3(θ.sub.0.sup.2 - θ.sub.x.sup.2)}             (26)'

Wherein θ_(x) is an angle made by a segment θ₁ x between a point x onthe screen drum 1 and the center O₁ and the segment O₁ C₁. θ_(x) can beany value, but here it is sufficient to consider that θ_(x) is in thecharging range, i.e. 0 ≦ θ_(x) ≦ 2θ₀. The equations (26) and (26)'change depending on the value of the θ_(x). For the equation (26) ifθ_(x) ≦ 1/2θ₀, δ(θ₁) ≦ 0 within a range of 0 ≦ θ₁ ≦ 2θ₀, and if θ_(x) >1/2θ₀, δ(θ₁) > 0. δ(θ₁) > 0 means that the dot positions formed on therecord medium as the point P in FIG. 5 moves from C₁ to B₁ through A₁precede the dot formed at the point C₂ on the record medium. Similarlyδ(θ₁) ≦ 0 means that the dot positions on the record carrier succeed thedot formed at the point C₂ on the record medium during the point P movesover the point C₁, A₁ and B₁.

Curves c, d, e and f in FIGS. 6 and 7 represent the equations (26) and(26)', respectively for θ_(x) = 1/4θ₀, θx = 1/2θ₀, θ_(x) = 3/4θ₀ andθ_(x) =θ₀. In FIGS. 6 and 7 the maximum amplitudes of the curvesrepresent amounts of dot prolongation within the range of 0 ≦ θ₁ ≦ 2θ₀,when the record medium is rotated at the peripheral speed v₂ (θ_(x)).

As can been seen from FIGS. 6 and 7 the amount of prolongation becomesdecreased as θ_(x) becomes larger and has the minimum value at a givenvalue of θ_(x). As θ_(x) becomes greater than this given value theamount of dot prolongation becomes extremely large. Next the optimalvalue for θ_(x) will be calculated.

(a) In case of 0 ≦θ_(x) ≦ 1/2θ₀

When the amount of dot prolongation is expressed as Δ(θ_(x)), thefollowing equation can be obtained: ##EQU26##

For r₂ < r₁ one can obtain the following equation: ##EQU27##

(b) In case of 1/2θ₀ < θ_(x) ≦ θ₀

When it is assumed that dδ(θ₁)/dθ ₁ = δ'(θ₁) and two roots of anequation δ'(θ₁) = 0 are k₁ (θ_(x)) and k₂ (θ_(x)), the followingequation can be derived:

    Δ(θ.sub.x) = |δ(k.sub.1) - δ (k.sub.2)| =  4βθ.sub.X.sup.3         (28)

for r₂ < r₁, the following equation may be derived:

    Δ(θ.sub.x) =  4|β|θ.sub.X.sup.3 (28)'

(3) in case of θ_(x) > θ₀ ##EQU28## is obtained. For r₂ < r₁,

    Δ(θ.sub.x) = 2|β|θ.sub.0 (√ 3θ.sub.x - θ.sub.0) (√3θ.sub.x + θ.sub.0) (29)'

can be derived.

The results obtained by the equations (27), (28) and (29) are shown inFIG. 8. The results which would be obtained from the equations (27)',(28)' and (29)' for r₂ < r₁ will be the same as those shown in FIG. 8only by converting α and β into |α| and |β|, respectively. From FIG. 8it is apparent that when θ_(x) = 1/2θ₀, i.e. ##EQU29## the amount of dotprolongation has the minimum value Δmin, ##EQU30## In these equations(30) and (31) W means the charging or printing width (W = 2r₁ θ₀).

In order to effect a high speed printing with the image formingapparatus having the screen drum the printing corona generator shouldhave a given finite charging or printing width W. For the given chargingwidth W the ratio of the rotating peripheral speeds of the screen drumand the record medium can be determined in accordance with the abovementioned equation (30) and then the charged dot has the minimum dotprolongation Δmin given by the equation (31) so as to obtain a sharpcopy image of high resolution. In some applications of the image formingapparatus explained hereinbefore it is desirable to establish variousallowable values Δ of the dot expansion. For instance, in case ofprinting characters and marks which are ordinarily used, it is notnecessary to decrease unnecessarily the dot prolongation Δ, but the dotprolongation up to about 100 μm may be allowable. However in case ofprinting special documents such as photographic documents the dotexpansion should be limited to about 20 - 80 μm. Even in these cases bydetermining the ratio of the speeds of the screen drum and the recordcarrier in accordance with the equation (30), the maximum charging widthWmax can be calculated from the equation (31) within each allowableamount of dot prolongation. The maximum charging width Wmax can berepresented as follows: ##EQU31##

As explained above in the image forming apparatus in which the ionstream is modulated with the electrostatic latent image formed on thephotosensitive screen drum so as to form a copy image on the recordmedium arranged opposite to the screen drum it is possible to minimizethe prolongation of dot by determining the rotating peripheralvelocities of the screen drum and the record medium in accordance withthe equation (30) for the given finite charging or printing width Wwhich is determined in accordance with the application and purpose ofthe image forming apparatus.

As will be clear from the following Table 1 the second term in theequation (30) is very small as compared with the first term and in manycases lower than 1% of the first term. Thus with considering variouslimitations upon designing the apparatus it is advantageous to make anallowable margine substantially equal to the second term for theequation (30). That is to say it is convenient to select the velocityratio k=v₂ /v₁ within the following range: in case of r₂ >r₁, ##EQU32##For such a velocity ratio the amount Δ of dot prolongation is given asfollows from FIG. 8. ##EQU33## The amount Δ of dot prolongation given bythe equation (34) is extremely smaller than that is obtained for thecase of v₁ =v₂.

Now the operational effect of the invention will shown in the followingTables.

                  TABLE I                                                         ______________________________________                                        W     r.sub.1                                                                              r.sub.2      k.sub.0 k.sub.2                                     (mm)  (mm)   (mm)   d (mm)                                                                              (1st term)                                                                            (2nd term)                                                                            k.sub.2 /k.sub.0                    ______________________________________                                               50    100    3     1.01478 0.00188 0.00186                                   100    120    5     1.00408 0.00019 0.00019                             20    100    200    5     1.01235 0.00047 0.00046                                   100    ∞                                                                              5     1.02500 0.00064 0.00063                                   100     80    5     0.99394 0.00034 0.00034                                    50    100    3     1.01478 0.00754 0.00743                                   100    120    5     1.00408 0.00075 0.00075                             40    100    200    5     1.01235 0.00188 0.00186                                   100    ∞                                                                              5     1.02500 0.00256 0.00250                                   100     80    5     0.99394 0.00135 0.00136                                    50    100    3     1.01478 0.01695 0.01671                                   100    120    5     1.00408 0.00169 0.00169                             60    100    200    5     1.01235 0.00424 0.00418                                   100    ∞                                                                              5     1.02500 0.00577 0.00563                                   100     80    5     0.99394 0.00304 0.00306                             ______________________________________                                        Note:                                                                          ##STR1##                                                                      ##STR2##                                                                 

Next the amounts Δ(mm) of dot prolongation will be calculated for threedifferent velocity ratios v₂ /V₁ =1, v₂ /v₁ =k₀ and v₂ /v₁ =k₀ +k₂ andfour different charging width W(mm). It should be noted that in thefollowing Tables 2 to 6, ##EQU34## is assumed.

Numerical Example 1

r₁ = 50 mm, r₂ = 100 mm, d = 3 mm

                  TABLE 2                                                         ______________________________________                                        W (mm)                                                                        Velocity     10       20       30     40                                      ______________________________________                                        v.sub.2 = v.sub.1                                                                          0.15406  0.34580  0.61289                                                                              0.99302                                 v.sub.2 = k.sub.0 v.sub.1                                                                  0.00628  0.05024  0.16954                                                                              0.40188                                 v.sub.2 = (k.sub.0  + k.sub.2)v.sub.1                                                      0.00157  0.01256  0.04239                                                                              0.10047                                 ______________________________________                                    

Numerical Example 2

r₁ = 100 mm, r₂ = 120 mm, d = 5 mm

                  TABLE 3                                                         ______________________________________                                        W(mm)                                                                         Velocity 10      20      30    40    50    60                                 ______________________________________                                        v.sub.2 = v.sub.1                                                                      0.04144 0.8665  0.13939                                                                             0.20341                                                                             0.28249                                                                             0.38039                            v.sub.2 = k.sub.0 v.sub.1                                                              0.00063 0.00502 0.01694                                                                             0.04015                                                                             0.07841                                                                             0.13549                            v.sub.2 =                                                                     (k.sub.0 + k.sub.2)v.sub.1                                                             0.00016 0.00125 0.00423                                                                             0.01004                                                                             0.01960                                                                             0.03387                            ______________________________________                                    

Numerical Example 3

r₁ = 100 mm, r₂ = 200 mm, d = 5 mm

                  TABLE 4                                                         ______________________________________                                        W(mm)                                                                         Velocity 10      20      30    40    50    60                                 ______________________________________                                        v.sub.2 = v.sub.1                                                                      0.12503 0.25946 0.41273                                                                             0.59422                                                                             0.81337                                                                             1.07958                            v.sub.2 = k.sub.0 v.sub.1                                                              0.00157 0.01255 0.04235                                                                             0.10040                                                                             0.19609                                                                             0.33884                            v.sub.2 =                                                                     (k.sub.0 + k.sub.2)v.sub.1                                                             0.00039 0.00314 0.01059                                                                             0.02510                                                                             0.04902                                                                             0.08471                            ______________________________________                                    

Numerical Example 4

r₁ = 100 mm, r₂ = ∞, d = 5 mm

                  TABLE 5                                                         ______________________________________                                        W(mm)                                                                         Velocity 10      20      30    40    50    60                                 ______________________________________                                        v.sub.2 = v.sub.1                                                                      0.25214 0.51718 0.80766                                                                             1.13667                                                                             1.51693                                                                             1.96125                            v.sub.2 = k.sub.0 v.sub.1                                                              0.00214 0.01708 0.05766                                                                             0.13667                                                                             0.26693                                                                             0.46125                            v.sub.2 =                                                                     (k.sub.0 + k.sub.2)v.sub.1                                                             0.00053 0.00427 0.01441                                                                             0.03417                                                                             0.06673                                                                             0.11531                            ______________________________________                                    

Numerical Example 5

r₁ = 100 mm, r₂ = 80 mm, d = 5 mm

                  TABLE 6                                                         ______________________________________                                        W(mm)                                                                         Velocity 10      20      30    40    50    60                                 ______________________________________                                        v.sub.2 = v.sub.1                                                                      0.06173 0.13022 0.21221                                                                             0.31447                                                                             0.44374                                                                             0.60678                            v.sub.2 = k.sub.0 v.sub.1                                                              0.00113 0.00901 0.03039                                                                             0.07204                                                                             0.14071                                                                             0.24315                            v.sub.2 =                                                                     (k.sub.0 + k.sub.2)v.sub.1                                                             0.00028 0.00225 0.00760                                                                             0.01801                                                                             0.03518                                                                             0.06079                            ______________________________________                                    

As can be seen from the above examples when the circumferential velocityv₂ of the record medium is selected to the optimum value, i.e.

    v.sub.2 = kv.sub.1 = (k.sub.0 +k.sub.2)v.sub.1,

the amount of dot expansion can be kept practically negligibly small,even if the charging width W is selected to 50 - 60 mm.

The present invention is not limited to the embodiments so fardescribed, but many modifications are possible within the scope of theinvention. For instance, in the above embodiment use is made oftransferring drum as the record medium, but it is possible to use a copypaper as the record medium. But in such a case since the paper could notconstitute the drum the paper is guided to move along an arcuate passagehaving the radius r₂. Moreover, the photosensitive screen is notnecessary to form the drum, but may be any other form. For example, thephotosensitive screen may be formed as a flexible belt and the belt maybe moved along the arcuate passage having the radius r₂ at the chargingor printing area in which the belt faces against the record medium.

What is claimed is:
 1. An electrophotographic apparatus comprisingaphotosensitive screen having a number of small apertures formed thereinand traveling through a printing area along an arcuate passage having aradius r₁ at a constant peripheral velocity v₁ ; a record mediumarranged opposite to the photosensitive screen with a distance d at theprinting area and traveling through the printing area along an arcuatepassage having a radius r₂ (r₂ ≠r₁) at a constant peripheral velocity v₂; means for forming on the photosensitive screen an electrostatic latentimage corresponding to a document to be copied; and means for generatinga corona ion stream which passes in the printing area through theapertures of the screen to the record medium and has a charging orprinting width W; wherein a ratio k of the peripheral velocities v₁ andv₂ of said photosensitive screen and record medium satisfies thefollowing equation: ##EQU35##
 2. An electrophotographic apparatusaccording to claim 1, wherein said ratio k of peripheral velocities ofthe photosensitive screen and record medium substantially satisfies thefollowing equation: ##EQU36##
 3. An electrophotographic apparatusaccording to claim 1, wherein said photosensitive screen is formed as aphotosensitive screen drum having the radius r₁ and rotating at theconstant peripheral velocity v₁.
 4. An electrophotographic apparatusaccording to claim 1, wherein said record medium is of a member fortransferring an electrostatic charge image.
 5. An electrophotographicapparatus according to claim 4, wherein said transferring member isformed as a drum which has the radius r₂ and rotates at the constantperipheral velocity v₂.
 6. An electrophotographic apparatus according toclaim 1, wherein said record medium is of a paper which is fed throughthe printing area along the arcuate passage having the radius r₂ at theperipheral velocity v₂.